HOMWORK PCA Example calculations. Please refer to slide from the INSY5339 class y XXY 2.5 2.4 0.69 0.49 0.4761 0.2401 0.3381 0.5 0.7 -13-12 1.7161 1.4641 1.5851 2.2 2.9 0.39 0.99 0.1521 0.9801 0.3861 1922 0.09 0.29 0.0081 0.0841 0.0261 3.1 3 1.291.09 1.6641 1.1881 1.4061 2.3 2.7 0.49 0.79 0.2401 0.6241 0.3871 2 1.6 0.19 -0.3 0.0361 0.0961 -0.0589 1 11 -0.8 -08 0.6561 0.6561 0.6561 1.5 1.6 -0.3 -0.3 0.0961 0.0961 0.0961 11 0.9 -0.7 -1 0.5041 1.0201 0.7171 Mean 1.81 1.91 Meanl 0 0 Var 0.616556 0.716556 Covariance 0.615444 PCA Methodology Given a dataset with n observations with m attributes: - Step 1: Calculate the mean of each attribute Step 2: From each value, subtract the mean of the attribute - Step 3: Calculate the covariance matrix - Step 4: Compute the eigen values of the covariance matrix; order them from largest to smallest Step 5: Compute Eigen vectors of the covariance matrix Step 6: Construct new dataset with new variables - Step 7: Dimensionality reduction step. Keep terms corresponding to the K largest Eigen values . HOMWORK PCA Example calculations. Please refer to slide from the INSY5339 class y XXY 2.5 2.4 0.69 0.49 0.4761 0.2401 0.3381 0.5 0.7 -13-12 1.7161 1.4641 1.5851 2.2 2.9 0.39 0.99 0.1521 0.9801 0.3861 1922 0.09 0.29 0.0081 0.0841 0.0261 3.1 3 1.291.09 1.6641 1.1881 1.4061 2.3 2.7 0.49 0.79 0.2401 0.6241 0.3871 2 1.6 0.19 -0.3 0.0361 0.0961 -0.0589 1 11 -0.8 -08 0.6561 0.6561 0.6561 1.5 1.6 -0.3 -0.3 0.0961 0.0961 0.0961 11 0.9 -0.7 -1 0.5041 1.0201 0.7171 Mean 1.81 1.91 Meanl 0 0 Var 0.616556 0.716556 Covariance 0.615444 PCA Methodology Given a dataset with n observations with m attributes: - Step 1: Calculate the mean of each attribute Step 2: From each value, subtract the mean of the attribute - Step 3: Calculate the covariance matrix - Step 4: Compute the eigen values of the covariance matrix; order them from largest to smallest Step 5: Compute Eigen vectors of the covariance matrix Step 6: Construct new dataset with new variables - Step 7: Dimensionality reduction step. Keep terms corresponding to the K largest Eigen values